Finish a fight in the battledome with or against a Jetsam. If you are looking for a jetsam to fight you can neomail any of the users of the below names and ask to fight their jetsam. Be sure to check to see if they have any rules about fighting first.
Update* This avatar has changed slightly since the battledome has been updated. At this time you need to have a Jetsam on YOUR account and battle with it.